Related papers: Generalized string-net models: A thorough expositi…

We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…

We investigate the following three consistency conditions for constructing string theories on orbifolds: i) the invariance of the energy-momentum tensors under twist operators, ii) the duality of amplitudes and iii) modular invariance of…

Twistor string models have been known for more than a decade now but have come back under the spotlight recently with the advent of the scattering equation formalism which has greatly generalized the scope of these models. A striking…

Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this paper we present a non-trivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We…

The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge…

We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact `decorated-string-net' framework to construct several classes of interesting models. In…

The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…

We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…

In this letter, we report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen stringnet model. The full Hamiltonian in our…

In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions.…

Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively…

The Su-Schrieffer-Heeger (SSH) model is a fundamental lattice model used to study topological physics. Here, we propose a new versatile one-dimensional (1D) lattice model that extends beyond the SSH model. Our 1D model breaks chiral…

We study indicators of broken time-reversal and parity symmetries in gapped topological phases of matter. We focus on phases realized by Levin-Wen string-net models, and generalize the string-net model to describe phases which break parity…

Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In…

All-order strong coupling simulations have been used to derive precise energies of string states in the confined phase of three dimensional Z(2) lattice gauge theory. The behavior of the ground state energy is here compared with predictions…

We construct 2+1-dimensional lattice models of symmetry-protected topological (SPT) phases with non-invertible symmetries and investigate their properties using tensor networks. These models, which we refer to as generalized cluster models,…

This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models. The tensionless limit is used to find a IIB supergravity background generated by a tensionless string.…

In this paper, we investigate the general properties of lattice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three 3D spin models…

In this paper we use trivial defects to define global taffy-like operations on string worldsheets, which preserve the field theory. We fold open and closed strings on a space X into open strings on products of multiple copies of X, and…

We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with…